What is the relationship between time to fall down and time to move over (x)?

Question

2 balls are released from 1 meter high at the exact same time. Ball 1 is simply dropped and ball 2 is launched off the edge of a desk from a ramp. Will both balls hit the floor at the same time? Why or why not?

Answer 1

They will both hit the ground at the same time. The reason is that there is *no* relationship between lateral (sideways) motion and the acceleration of gravity. Since they are at 'right angles' to each other, they have no effect on each other.


Doug

Answer 2

If you meant that ball 2 was released to roll down a ramp prior to ball 1 being dropped as ball 2 falls over the desk from a height of 1 meter, then ball 2 would have had an initial downward vertical velocity, whereas ball 1 had NO initial downward vertical velocity. That means ball 2 will hit the ground first.

Now if you meant that both balls are released at the same time, but ball 2 rolls down a ramp instead of being dropped, then the answer is that both balls will hit the ground at the same time. However, this result must also assume that the ramp is frictionless and that air friction is also neglegible.

The result of the motion of the two balls totally depends on what forces are acting on them and what are their initial conditions. If we assumed that their initial conditions are identical, i.e. position is at (x=0,y=0) and velocities are (Vx=0, Vy=0), and then if the forces acting on them are also completely identical, i.e. only the gravitational force acting in the -y direction. Then the time it takes for the balls to hit the ground will be exactly the same. The ramp does nothing except to cause ball to have a lateral motion along the x-direction that is completely independent of the motion in the y-direction.

Of course, if there were friction along the surface of the ramp, then that would have slowed ball 2 down, and then it would hit the ground later than ball 1.

Answer 3

The difference between the motions of the two balls is in their initial condition.

The first ball has no initial horizontal speed, where as the second ball has a horizontal speed as it is launched from a table top.

As far as the vertical motion is concerned both balls have the initial vertical speed of zero.

The only force acting on the two is the vertical acceleration due to gravity. We assume that there is no friction or any other force acting on them.

Therefore, the time to reach the ground will be the same for both balls.

“How much horizontal distance both have moved?” is not at all concerned to us, because the horizontal distance is determined by the horizontal speed times ( x) the time taken for the vertical displacement which is the same for both the balls.

Answer 4

Always, Ball 1 will hit the ground first...
Coz ball 1 is falling downwards,, ball 2 is travelling a trajectory path...

An analytical understanding will be that:
Ball 1 travels only in y-axis... will hit first)
Ball 2 travels both in x-axis and y-axis components (so ur time of travel is roughly the hypotenuse of the right triangle - which is longest.... while ball 1 has to cover only Opposite side (straight doown)